《TABLES OF THE MATHEMATICAL FUNCTIONS ARITHMETICAL TABLES》

CHAPTER 1．THE ARITHMETICAL FUNCTIONS1

1．Introduction1

2．Integral Powers2

3．The Reciprocal Functions3

4．Fractional Powers6

5．Complex Numbers7

6．The Power Function10

7．Computation of the Functions13

8．Multiplication Tables18

CHAPTER 2．MATHEMATICAL CONSTANTS19

1．The Mathematical Constants19

2．The History of the Computation of π19

3．The Computation of e25

4．The Computation of Euler＇s Constant(C or γ)28

5．The Value of logeπ29

6．The Modulus M,and Other Logarithms30

7．Square and Cube Roots32

8．Algebraic and Transcendental Numbers33

CHAPTER 3．THE SOLUTION OF EQUATIONS37

1．Introduction37

2．The Newton-Raphson Method of Solution37

3．Extension of the Newton-Raphson Method to Systems of Equations40

4．The Theory of Equations43

5．The Quadratic Equation43

6．The Cubic Equation45

7．Solution of Cubic Equations by Means of Circular Functions48

8．Tabular Solution of the Irreducible Case of the Cubic50

9．Tabular Solution of the General Cubic with Real Coefficients61

10．The Quartic Equation63

11．Homer＇s Method for Approximating Real Roots71

12．The Root-Squaring Method of Solving Equations78

CHAPTER 4．TRANSCENDENTAL EQUATIONS84

1．Transcendental Equations84

2．General Methods of Solution85

3．The Method of Iteration86

4．The Inversion Formula of Lagrange89

5．The Roots of Some Special Equations94

TABLES97

Table 1．Special Values of Mathematical Constants99

Table 2．Squares and Cubes107

Table 3．Values of Reciprocals197

Table 4．Values of Reciprocals209

Table 5．Values of the Fraction m/n271

Table 6．Square Roots-Values of x1/2 and(10x)1/2297

Table 7．Square Roots-Values of x1/2 and(10x)1/2319

Table 8．Cube Roots-Values of x1/3,(10x)1/3,and(100x)1/3411

Table 9．Cube Roots-Values of x1/3443

Table 10．Values of x3/2,(10x)3/2,and their Reciprocals505

Table 11．Binomial Coefficients511

Table 12．Powers of Integers543

INDEX OF NAMES551

INDEX OF SUBJECTS553